--- res: bibo_abstract: - For any n≥3, let F ∈ Z[X0,...,Xn ] be a form of degree d *≥5 that defines a non-singular hypersurface X ⊂ Pn . The main result in this paper is a proof of the fact that the number N (F ; B) of Q-rational points on X which have height at most B satisfiesN (F ; B) = Od,ε,n (Bn −1+ε ), for any ε > 0. The implied constant in this estimate depends at most upon d, ε and n. New estimates are also obtained for the number of representations of a positive integer as the sum of three dth powers, and for the paucity of integer solutions to equal sums of like polynomials.*@eng bibo_authorlist: - foaf_Person: foaf_givenName: Timothy D foaf_name: Timothy Browning foaf_surname: Browning foaf_workInfoHomepage: http://www.librecat.org/personId=35827D50-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-8314-0177 - foaf_Person: foaf_givenName: Roger foaf_name: Heath-Brown, Roger foaf_surname: Heath Brown bibo_doi: 10.1112/S0024609305018412 bibo_issue: '3' bibo_volume: 38 dct_date: 2006^xs_gYear dct_publisher: Wiley-Blackwell@ dct_title: The density of rational points on non-singular hypersurfaces, I@ ...